Continuous approximation formulas for location problems

Abstract

The majority of research in the continuous approximation paradigm has emphasized routing problems, such as the travelling salesman problem and the vehicle routing problem. This article instead focuses on continuous approximation formulas for problems involving location, specifically the k$$ k $$‐medians, k$$ k $$‐dispersion, and generalized minimum spanning tree problems. We contribute bounds for constants that describe the growth rate of the cost of these problems as the number of demand points becomes large, and conduct computational experiments that verify that they provide a good approximation in practice.